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Simplifying (5 + -1x)(x + 7.3) = 0 Reorder the terms: (5 + -1x)(7.3 + x) = 0 Multiply (5 + -1x) * (7.3 + x) (5(7.3 + x) + -1x * (7.3 + x)) = 0 ((7.3 * 5 + x * 5) + -1x * (7.3 + x)) = 0 ((36.5 + 5x) + -1x * (7.3 + x)) = 0 (36.5 + 5x + (7.3 * -1x + x * -1x)) = 0 (36.5 + 5x + (-7.3x + -1x2)) = 0 Combine like terms: 5x + -7.3x = -2.3x (36.5 + -2.3x + -1x2) = 0 Solving 36.5 + -2.3x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36.5 + 2.3x + x2 = 0 Move the constant term to the right: Add '36.5' to each side of the equation. -36.5 + 2.3x + 36.5 + x2 = 0 + 36.5 Reorder the terms: -36.5 + 36.5 + 2.3x + x2 = 0 + 36.5 Combine like terms: -36.5 + 36.5 = 0.0 0.0 + 2.3x + x2 = 0 + 36.5 2.3x + x2 = 0 + 36.5 Combine like terms: 0 + 36.5 = 36.5 2.3x + x2 = 36.5 The x term is 2.3x. Take half its coefficient (1.15). Square it (1.3225) and add it to both sides. Add '1.3225' to each side of the equation. 2.3x + 1.3225 + x2 = 36.5 + 1.3225 Reorder the terms: 1.3225 + 2.3x + x2 = 36.5 + 1.3225 Combine like terms: 36.5 + 1.3225 = 37.8225 1.3225 + 2.3x + x2 = 37.8225 Factor a perfect square on the left side: (x + 1.15)(x + 1.15) = 37.8225 Calculate the square root of the right side: 6.15 Break this problem into two subproblems by setting (x + 1.15) equal to 6.15 and -6.15.Subproblem 1
x + 1.15 = 6.15 Simplifying x + 1.15 = 6.15 Reorder the terms: 1.15 + x = 6.15 Solving 1.15 + x = 6.15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.15' to each side of the equation. 1.15 + -1.15 + x = 6.15 + -1.15 Combine like terms: 1.15 + -1.15 = 0.00 0.00 + x = 6.15 + -1.15 x = 6.15 + -1.15 Combine like terms: 6.15 + -1.15 = 5 x = 5 Simplifying x = 5Subproblem 2
x + 1.15 = -6.15 Simplifying x + 1.15 = -6.15 Reorder the terms: 1.15 + x = -6.15 Solving 1.15 + x = -6.15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.15' to each side of the equation. 1.15 + -1.15 + x = -6.15 + -1.15 Combine like terms: 1.15 + -1.15 = 0.00 0.00 + x = -6.15 + -1.15 x = -6.15 + -1.15 Combine like terms: -6.15 + -1.15 = -7.3 x = -7.3 Simplifying x = -7.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, -7.3}
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